Exploring the Connection between Uncertainty and Relativity in Physics

[Holystromboli]

I'm still pretty much a virgin when it comes to the serious study of physics, so I apologize if this question is a bit ridiculous. Is the lack of specificity of velocity and position according to the uncertainty principle somehow related to the lack of meaning of velocity without an independent FoR at relativistic scales? I.e. It seems like there are parallels between the concept of a particle's position/velocity being undetermined until it is observed/measured and the lack of meaning of constant velocity without an opposing FoR in special relativity. At large scales, an object O1 in FoR1 doesn't technically have a velocity until it is measured in relation to object O2 with FoR2, right? Does this question make sense? I realize that we are talking about two entirely different theoretical frameworks, that trying to apply any type of intuitive reasoning to complex physics is always a recipe for disaster, and that some of my basic assumptions here are probably irrelevant, invalid, or worse, but I thought and still think it's a fun question... :)

 

[PeterDonis]

Is the lack of specificity of velocity and position according to the uncertainty principle somehow related to the lack of meaning of velocity without an independent FoR at relativistic scales?

No. They're two different things. The first is a quantum phenomenon; the second is classical.

Also, you are somewhat misstating the second item. See below.

At large scales, an object O1 in FoR1 doesn't technically have a velocity until it is measured in relation to object O2 with FoR2, right

It's not a matter of measurement; it's a matter of definition. Velocity is relative; there's no such thing as "the velocity of an object" by ltself. Only the velocity of one object relative to another has meaning. But once you've made the definition correctly, the relative velocity of two objects exists, in classical special relativity, whether or not it is measured and regardless of who measures it. (Btw, this applies for all relative velocities, not just relativistic ones.)

 

[Holystromboli]

I think I see what you mean. The position/velocity of the particle is actually determined by the measurement from a series of probabilities in the quantum world whereas an object's position and velocity on large scales... Well I'm struggling to put words to my understanding, but I think I get the gist... :)
Thanks for the reply!

 

[PeterDonis]

The position/velocity of the particle is actually determined by the measurement from a series of probabilities in the quantum world whereas an object's position and velocity on large scales...

There's more to the quantum issue than that. At the quantum level, it's not just that you can't measure position and velocity at the same time: it's that there aren't any possible states of the particle that have both a definite position and a definite velocity. And states that have a narrower spread in position (i.e., a more precise position) have a wider spread in velocity, and vice versa. A measurement of position is a measurement that kicks the particle into a state with a narrower spread in position (in the idealized limit, a perfectly precise position) and therefore a wider spread in velocity (in the idealized limit, the velocity spread is infinite). A measurement of velocity is one that kicks the particle into a state with a narrower spread in velocity, and therefore a wider spread in position. There's nothing you can do to the particle that makes both the spread in position and velocity narrower; it simply isn't possible because there are no such states for the particle to be kicked into.

At the classical level, every state of the particle has both a definite position and a definite velocity. So no matter what you do to the particle--measure it, don't measure it, whatever--it is going to have a definite position and a definite velocity. But when you take relativity into account, these definite positions and velocities are frame-dependent; change frames and you change their values. But their values in every frame are always definite, no matter what state the particle is in.

 

[Holystromboli]

Great response. Thanks for taking the time to set me straight. :)
I still can't help myself from seeing parallels between the two concepts, but I think I understand your explanation of why they're really nothing at all alike. At the quantum level it's simply impossible to measure both values simultaneously. Reality as we know it prevents it. In classical systems, determination of velocity requires an external reference, but the position and velocity of the object are solid concepts even if they're values change as you change your frame of reference. Is that close to what you're saying?

 

[PeterDonis]

the position and velocity of the object are solid concepts

Instead of "are solid concepts" I would say "have definite values". In QM, position and velocity are both "solid concepts" in the sense of being perfectly well-defined observables; it's just that there aren't any states where both of those observables have definite values.

 

[Holystromboli]

Good call. Thanks for the correction. I have a long way to go before I'll be able to effectively articulate what's going on in my head... :)